Outside In

Discusses the problem of turning a sphere inside out without creating sharp bends or creases, illustrating an application of turning points.

The computer animation Outside In explains the amazing discovery, made by Steve Smale in 1957, that a sphere can be turned inside out by means of smooth motions and self-intersections. Through a combination of dialogue and exposition accessible to anyone who has some interest in mathematics, Outside In builds up to the grand finale: Bill Thurston's "corrugations" method of turning the sphere inside out.